Question

The size of a microscopic particle is 1 micron and its mass is $6\times {10}^{-13}$g. If its position may be measured to within 0.1 % of its size, the uncertainty in velocity $\left(inc{m}^{-1}\right)$ is approximately?

• A. $\frac{{10}^{-7}}{4\pi }$
• B. $\frac{{10}^{-5}}{4\pi }$
• C. ${10}^{-5}$
• D. ${10}^{-8}$

Answer 1

The correct option is A $\frac{{10}^{-7}}{4\pi }$

$\Delta x$ = uncertainty in position

Heisenberg uncertainty equation is $\Delta x\left(m\Delta v\right)=h/4\pi$

$\Delta x$ = 0.1% of size of particle = $0.1\times 1\times {10}^{-}12/100\times {10}^{-}2$ m = ${10}^{-}17$ $m^{-}1$

${10}^{-}17\times 6\times {10}^{-}15\times \Delta v=6.626\times {10}^{-}34/4\pi$

$\Delta v={10}^{-}5/4\pi$ $m^{-}1$

or $\Delta v={10}^{-}7/4\pi$ in $c{m}^{-}1$